TSTP Solution File: GRP685+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP685+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:20:36 EDT 2022
% Result : Theorem 0.88s 1.13s
% Output : Refutation 0.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP685+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 06:09:12 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.88/1.13 ============================== Prover9 ===============================
% 0.88/1.13 Prover9 (32) version 2009-11A, November 2009.
% 0.88/1.13 Process 16472 was started by sandbox on n021.cluster.edu,
% 0.88/1.13 Tue Jun 14 06:09:13 2022
% 0.88/1.13 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_16319_n021.cluster.edu".
% 0.88/1.13 ============================== end of head ===========================
% 0.88/1.13
% 0.88/1.13 ============================== INPUT =================================
% 0.88/1.13
% 0.88/1.13 % Reading from file /tmp/Prover9_16319_n021.cluster.edu
% 0.88/1.13
% 0.88/1.13 set(prolog_style_variables).
% 0.88/1.13 set(auto2).
% 0.88/1.13 % set(auto2) -> set(auto).
% 0.88/1.13 % set(auto) -> set(auto_inference).
% 0.88/1.13 % set(auto) -> set(auto_setup).
% 0.88/1.13 % set(auto_setup) -> set(predicate_elim).
% 0.88/1.13 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.88/1.13 % set(auto) -> set(auto_limits).
% 0.88/1.13 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.88/1.13 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.88/1.13 % set(auto) -> set(auto_denials).
% 0.88/1.13 % set(auto) -> set(auto_process).
% 0.88/1.13 % set(auto2) -> assign(new_constants, 1).
% 0.88/1.13 % set(auto2) -> assign(fold_denial_max, 3).
% 0.88/1.13 % set(auto2) -> assign(max_weight, "200.000").
% 0.88/1.13 % set(auto2) -> assign(max_hours, 1).
% 0.88/1.13 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.88/1.13 % set(auto2) -> assign(max_seconds, 0).
% 0.88/1.13 % set(auto2) -> assign(max_minutes, 5).
% 0.88/1.13 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.88/1.13 % set(auto2) -> set(sort_initial_sos).
% 0.88/1.13 % set(auto2) -> assign(sos_limit, -1).
% 0.88/1.13 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.88/1.13 % set(auto2) -> assign(max_megs, 400).
% 0.88/1.13 % set(auto2) -> assign(stats, some).
% 0.88/1.13 % set(auto2) -> clear(echo_input).
% 0.88/1.13 % set(auto2) -> set(quiet).
% 0.88/1.13 % set(auto2) -> clear(print_initial_clauses).
% 0.88/1.13 % set(auto2) -> clear(print_given).
% 0.88/1.13 assign(lrs_ticks,-1).
% 0.88/1.13 assign(sos_limit,10000).
% 0.88/1.13 assign(order,kbo).
% 0.88/1.13 set(lex_order_vars).
% 0.88/1.13 clear(print_given).
% 0.88/1.13
% 0.88/1.13 % formulas(sos). % not echoed (8 formulas)
% 0.88/1.13
% 0.88/1.13 ============================== end of input ==========================
% 0.88/1.13
% 0.88/1.13 % From the command line: assign(max_seconds, 300).
% 0.88/1.13
% 0.88/1.13 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.88/1.13
% 0.88/1.13 % Formulas that are not ordinary clauses:
% 0.88/1.13 1 (all A ld(A,mult(A,A)) = A) # label(f01) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.13 2 (all A rd(mult(A,A),A) = A) # label(f02) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.13 3 (all B all A mult(A,ld(A,B)) = ld(A,mult(A,B))) # label(f03) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.13 4 (all B all A mult(rd(A,B),B) = rd(mult(A,B),B)) # label(f04) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.13 5 (all D all C all B all A ld(ld(A,B),mult(ld(A,B),mult(C,D))) = mult(ld(A,mult(A,C)),D)) # label(f05) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.13 6 (all D all C all B all A rd(mult(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,rd(mult(B,D),D))) # label(f06) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.13 7 (all B all A ld(A,mult(A,ld(B,B))) = rd(mult(rd(A,A),B),B)) # label(f07) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.13 8 -(all X6 all X7 all X8 (rd(mult(X6,ld(X7,X8)),ld(X7,X8)) = rd(mult(X6,X8),X8) & rd(mult(X6,rd(X7,X8)),rd(X7,X8)) = rd(mult(X6,X8),X8))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.88/1.13
% 0.88/1.13 ============================== end of process non-clausal formulas ===
% 0.88/1.13
% 0.88/1.13 ============================== PROCESS INITIAL CLAUSES ===============
% 0.88/1.13
% 0.88/1.13 ============================== PREDICATE ELIMINATION =================
% 0.88/1.13
% 0.88/1.13 ============================== end predicate elimination =============
% 0.88/1.13
% 0.88/1.13 Auto_denials:
% 0.88/1.13 % copying label goals to answer in negative clause
% 0.88/1.13
% 0.88/1.13 Term ordering decisions:
% 0.88/1.13 Function symbol KB weights: c1=1. c2=1. c3=1. mult=1. ld=1. rd=1.
% 0.88/1.13
% 0.88/1.13 ============================== end of process initial clauses ========
% 0.88/1.13
% 0.88/1.13 ============================== CLAUSES FOR SEARCH ====================
% 0.88/1.13
% 0.88/1.13 ============================== end of clauses for search =============
% 0.88/1.13
% 0.88/1.13 ============================== SEARCH ================================
% 0.88/1.13
% 0.88/1.13 % Starting search at 0.01 seconds.
% 0.88/1.13
% 0.88/1.13 ============================== PROOF =================================
% 0.88/1.13 % SZS status Theorem
% 0.88/1.13 % SZS output start Refutation
% 0.88/1.13
% 0.88/1.13 % Proof 1 at 0.14 (+ 0.01) seconds: goals.
% 0.88/1.13 % Length of proof is 99.
% 0.88/1.13 % Level of proof is 20.
% 0.88/1.13 % Maximum clause weight is 35.000.
% 0.88/1.13 % Given clauses 94.
% 0.88/1.13
% 0.88/1.13 1 (all A ld(A,mult(A,A)) = A) # label(f01) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.13 2 (all A rd(mult(A,A),A) = A) # label(f02) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.13 3 (all B all A mult(A,ld(A,B)) = ld(A,mult(A,B))) # label(f03) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.13 4 (all B all A mult(rd(A,B),B) = rd(mult(A,B),B)) # label(f04) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.13 5 (all D all C all B all A ld(ld(A,B),mult(ld(A,B),mult(C,D))) = mult(ld(A,mult(A,C)),D)) # label(f05) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.13 6 (all D all C all B all A rd(mult(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,rd(mult(B,D),D))) # label(f06) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.13 7 (all B all A ld(A,mult(A,ld(B,B))) = rd(mult(rd(A,A),B),B)) # label(f07) # label(axiom) # label(non_clause). [assumption].
% 0.88/1.13 8 -(all X6 all X7 all X8 (rd(mult(X6,ld(X7,X8)),ld(X7,X8)) = rd(mult(X6,X8),X8) & rd(mult(X6,rd(X7,X8)),rd(X7,X8)) = rd(mult(X6,X8),X8))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.88/1.13 9 ld(A,mult(A,A)) = A # label(f01) # label(axiom). [clausify(1)].
% 0.88/1.13 10 rd(mult(A,A),A) = A # label(f02) # label(axiom). [clausify(2)].
% 0.88/1.13 11 ld(A,mult(A,B)) = mult(A,ld(A,B)) # label(f03) # label(axiom). [clausify(3)].
% 0.88/1.13 12 rd(mult(A,B),B) = mult(rd(A,B),B) # label(f04) # label(axiom). [clausify(4)].
% 0.88/1.13 13 rd(mult(rd(A,A),B),B) = ld(A,mult(A,ld(B,B))) # label(f07) # label(axiom). [clausify(7)].
% 0.88/1.13 14 mult(rd(rd(A,A),B),B) = mult(A,ld(A,ld(B,B))). [copy(13),rewrite([12(3),11(6)])].
% 0.88/1.13 15 ld(ld(A,B),mult(ld(A,B),mult(C,D))) = mult(ld(A,mult(A,C)),D) # label(f05) # label(axiom). [clausify(5)].
% 0.88/1.13 16 mult(ld(A,B),ld(ld(A,B),mult(C,D))) = mult(mult(A,ld(A,C)),D). [copy(15),rewrite([11(5),11(7)])].
% 0.88/1.13 17 rd(mult(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,rd(mult(B,D),D)) # label(f06) # label(axiom). [clausify(6)].
% 0.88/1.13 18 mult(rd(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,mult(rd(B,D),D)). [copy(17),rewrite([12(5),12(7)])].
% 0.88/1.13 19 rd(mult(c1,ld(c2,c3)),ld(c2,c3)) != rd(mult(c1,c3),c3) | rd(mult(c1,rd(c2,c3)),rd(c2,c3)) != rd(mult(c1,c3),c3) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(8)].
% 0.88/1.13 20 mult(rd(c1,ld(c2,c3)),ld(c2,c3)) != mult(rd(c1,c3),c3) | mult(rd(c1,rd(c2,c3)),rd(c2,c3)) != mult(rd(c1,c3),c3) # answer(goals). [copy(19),rewrite([12(9),12(14),12(24),12(29)])].
% 0.88/1.13 21 mult(A,ld(A,A)) = A. [back_rewrite(9),rewrite([11(2)])].
% 0.88/1.13 22 mult(rd(A,A),A) = A. [back_rewrite(10),rewrite([12(2)])].
% 0.88/1.13 25 mult(ld(A,B),ld(ld(A,B),ld(ld(A,B),mult(C,D)))) = ld(ld(A,B),mult(mult(A,ld(A,C)),D)). [para(16(a,1),11(a,1,2)),flip(a)].
% 0.88/1.13 26 mult(mult(A,ld(A,B)),ld(mult(A,ld(A,B)),mult(C,D))) = mult(mult(A,ld(A,C)),D). [para(11(a,1),16(a,1,1)),rewrite([11(4)])].
% 0.88/1.13 27 mult(ld(A,B),mult(ld(A,B),ld(ld(A,B),C))) = mult(mult(A,ld(A,ld(A,B))),C). [para(11(a,1),16(a,1,2))].
% 0.88/1.13 33 mult(rd(mult(A,B),mult(rd(C,D),D)),mult(rd(C,D),D)) = mult(A,mult(rd(B,D),D)). [para(12(a,1),18(a,1,1,2)),rewrite([12(6)])].
% 0.88/1.13 35 mult(rd(rd(A,A),B),mult(rd(B,C),C)) = mult(A,mult(rd(ld(A,ld(B,B)),C),C)). [para(14(a,1),18(a,1,1,1)),rewrite([18(7)]),flip(a)].
% 0.88/1.13 39 mult(A,ld(A,ld(A,A))) = ld(A,A). [para(21(a,1),11(a,1,2)),flip(a)].
% 0.88/1.13 40 mult(rd(A,ld(A,A)),ld(A,A)) = rd(A,ld(A,A)). [para(21(a,1),12(a,1,1)),flip(a)].
% 0.88/1.13 42 mult(rd(A,rd(B,C)),rd(B,C)) = mult(A,mult(rd(ld(A,A),C),C)). [para(21(a,1),18(a,1,1,1))].
% 0.88/1.13 44 rd(A,A) = ld(A,A). [para(22(a,1),12(a,1,1)),rewrite([14(4),39(4)])].
% 0.88/1.13 45 mult(ld(A,A),A) = A. [para(22(a,1),12(a,2)),rewrite([12(2),44(1)])].
% 0.88/1.13 46 mult(A,ld(A,ld(ld(A,A),ld(A,A)))) = ld(A,A). [para(22(a,1),14(a,1)),rewrite([44(1),44(2),44(3)]),flip(a)].
% 0.88/1.13 47 mult(ld(A,B),ld(ld(A,B),C)) = mult(mult(A,ld(A,ld(C,C))),C). [para(22(a,1),16(a,1,2,2)),rewrite([44(5)])].
% 0.88/1.13 50 mult(rd(ld(A,A),B),mult(rd(B,C),C)) = mult(A,mult(rd(ld(A,ld(B,B)),C),C)). [back_rewrite(35),rewrite([44(1)])].
% 0.88/1.13 54 mult(rd(ld(A,A),B),B) = mult(A,ld(A,ld(B,B))). [back_rewrite(14),rewrite([44(1)])].
% 0.88/1.13 55 mult(rd(A,rd(B,C)),rd(B,C)) = mult(A,mult(A,ld(A,ld(C,C)))). [back_rewrite(42),rewrite([54(7)])].
% 0.88/1.13 57 mult(mult(A,ld(A,B)),ld(mult(A,ld(A,B)),ld(mult(A,ld(A,B)),mult(C,D)))) = ld(mult(A,ld(A,B)),mult(mult(A,ld(A,C)),D)). [para(11(a,1),25(a,1,1)),rewrite([11(4),11(6),11(12)])].
% 0.88/1.13 65 ld(ld(A,B),mult(mult(A,ld(A,ld(C,C))),C)) = mult(ld(A,B),ld(ld(A,B),ld(ld(A,B),C))). [para(45(a,1),25(a,1,2,2,2)),flip(a)].
% 0.88/1.13 82 mult(mult(A,ld(A,B)),C) = mult(A,ld(A,mult(B,C))). [para(21(a,1),26(a,1,1)),rewrite([21(2)]),flip(a)].
% 0.88/1.13 83 mult(A,ld(A,mult(B,ld(mult(A,ld(A,B)),C)))) = mult(A,ld(A,C)). [para(21(a,1),26(a,1,2,2)),rewrite([82(6),82(10),21(8)])].
% 0.88/1.13 84 mult(A,mult(A,ld(A,B))) = mult(A,B). [para(21(a,1),26(a,2,1)),rewrite([82(7),83(7),11(2)])].
% 0.88/1.13 86 mult(A,ld(A,mult(ld(A,A),B))) = mult(ld(A,A),B). [para(39(a,1),26(a,2,1)),rewrite([82(8),83(8)])].
% 0.88/1.13 96 mult(ld(A,B),ld(ld(A,B),ld(ld(A,B),C))) = ld(ld(A,B),mult(A,ld(A,C))). [back_rewrite(65),rewrite([82(5),45(3)]),flip(a)].
% 0.88/1.13 101 ld(mult(A,ld(A,B)),mult(A,ld(A,mult(C,D)))) = mult(A,ld(A,ld(mult(A,ld(A,B)),mult(C,D)))). [back_rewrite(57),rewrite([82(10),83(10),82(11)]),flip(a)].
% 0.88/1.13 103 mult(ld(A,B),ld(ld(A,B),C)) = mult(A,ld(A,C)). [back_rewrite(47),rewrite([82(8),45(6)])].
% 0.88/1.13 106 mult(ld(A,B),mult(A,ld(A,C))) = mult(A,ld(A,mult(ld(A,B),C))). [back_rewrite(27),rewrite([103(5),82(8)])].
% 0.88/1.13 108 mult(rd(A,rd(B,C)),rd(B,C)) = mult(A,ld(C,C)). [back_rewrite(55),rewrite([84(8)])].
% 0.88/1.13 109 ld(ld(A,B),mult(A,ld(A,C))) = mult(A,ld(A,ld(ld(A,B),C))). [back_rewrite(96),rewrite([103(6)]),flip(a)].
% 0.88/1.13 117 mult(rd(c1,ld(c2,c3)),ld(c2,c3)) != mult(rd(c1,c3),c3) | mult(rd(c1,c3),c3) != mult(c1,ld(c3,c3)) # answer(goals). [back_rewrite(20),rewrite([108(24)]),flip(b)].
% 0.88/1.13 118 mult(mult(A,B),ld(C,C)) = mult(A,mult(rd(B,C),C)). [back_rewrite(18),rewrite([108(5)])].
% 0.88/1.13 139 mult(A,ld(A,ld(mult(A,ld(A,B)),mult(B,C)))) = mult(A,ld(A,C)). [para(82(a,1),11(a,1,2)),rewrite([101(6),82(12),83(12)])].
% 0.88/1.13 140 mult(A,ld(A,mult(mult(A,B),C))) = mult(mult(A,B),C). [para(11(a,1),82(a,1,1,2)),rewrite([84(3)]),flip(a)].
% 0.88/1.13 152 ld(ld(A,A),ld(A,A)) = ld(A,A). [para(39(a,1),86(a,1,2,2)),rewrite([46(5),39(8)]),flip(a)].
% 0.88/1.13 162 mult(A,mult(rd(B,ld(C,C)),ld(C,C))) = mult(A,mult(rd(B,C),C)). [para(40(a,1),33(a,1,1,2)),rewrite([40(8),108(7),152(4),118(3)]),flip(a)].
% 0.88/1.13 187 mult(A,ld(A,ld(A,B))) = ld(A,B). [para(103(a,1),21(a,1))].
% 0.88/1.13 189 mult(A,ld(A,mult(ld(A,B),C))) = mult(ld(A,B),C). [para(103(a,1),84(a,1,2)),rewrite([106(4)])].
% 0.88/1.13 193 mult(ld(A,B),mult(A,ld(A,C))) = mult(ld(A,B),C). [back_rewrite(106),rewrite([189(8)])].
% 0.88/1.13 195 mult(A,ld(A,ld(mult(A,ld(A,B)),C))) = ld(mult(A,ld(A,B)),C). [para(187(a,1),82(a,1)),rewrite([83(12)]),flip(a)].
% 0.88/1.13 196 mult(A,ld(A,ld(ld(A,B),C))) = ld(ld(A,B),C). [para(187(a,1),103(a,1)),flip(a)].
% 0.88/1.13 197 ld(mult(A,ld(A,B)),mult(B,C)) = mult(A,ld(A,C)). [back_rewrite(139),rewrite([195(6)])].
% 0.88/1.13 199 ld(ld(A,B),mult(A,ld(A,C))) = ld(ld(A,B),C). [back_rewrite(109),rewrite([196(8)])].
% 0.88/1.13 202 mult(rd(ld(A,A),mult(B,C)),mult(mult(rd(B,C),C),C)) = mult(A,mult(rd(ld(A,ld(mult(B,C),mult(B,C))),C),C)). [para(12(a,1),50(a,1,2,1))].
% 0.88/1.13 205 mult(rd(ld(A,A),ld(B,B)),mult(B,ld(B,ld(C,C)))) = mult(A,mult(rd(ld(A,ld(B,B)),C),C)). [para(54(a,1),50(a,1,2)),rewrite([152(10)])].
% 0.88/1.13 208 mult(rd(A,ld(B,B)),ld(B,B)) = mult(A,ld(B,B)). [para(44(a,1),108(a,1,1,2)),rewrite([44(3)])].
% 0.88/1.13 209 mult(rd(A,B),ld(B,B)) = rd(A,B). [para(44(a,1),108(a,1,1)),rewrite([45(5)]),flip(a)].
% 0.88/1.13 211 mult(ld(A,A),ld(B,B)) = mult(A,ld(A,ld(B,B))). [para(54(a,1),108(a,2)),rewrite([108(7),208(5),152(6)])].
% 0.88/1.13 215 mult(A,mult(rd(B,C),C)) = mult(A,mult(B,ld(C,C))). [back_rewrite(162),rewrite([208(4)]),flip(a)].
% 0.88/1.13 217 rd(A,ld(A,A)) = A. [back_rewrite(40),rewrite([208(4),21(2)]),flip(a)].
% 0.88/1.13 226 mult(rd(ld(A,A),ld(B,B)),mult(B,ld(B,ld(C,C)))) = mult(A,mult(ld(A,ld(B,B)),ld(C,C))). [back_rewrite(205),rewrite([215(12)])].
% 0.88/1.13 227 mult(rd(ld(A,A),mult(B,C)),mult(mult(rd(B,C),C),C)) = mult(A,mult(ld(A,ld(mult(B,C),mult(B,C))),ld(C,C))). [back_rewrite(202),rewrite([215(14)])].
% 0.88/1.13 256 mult(mult(A,B),ld(C,C)) = mult(A,mult(B,ld(C,C))). [back_rewrite(118),rewrite([215(6)])].
% 0.88/1.13 260 mult(rd(A,B),B) = mult(A,ld(B,B)). [para(217(a,1),108(a,1,1,2)),rewrite([217(3),152(5)])].
% 0.88/1.13 270 mult(rd(ld(A,A),mult(B,C)),mult(mult(B,ld(C,C)),C)) = mult(A,mult(ld(A,ld(mult(B,C),mult(B,C))),ld(C,C))). [back_rewrite(227),rewrite([260(5)])].
% 0.88/1.13 277 mult(c1,ld(ld(c2,c3),ld(c2,c3))) != mult(c1,ld(c3,c3)) # answer(goals). [back_rewrite(117),rewrite([260(9),260(14),260(20)]),xx(b)].
% 0.88/1.13 280 rd(mult(A,B),B) = mult(A,ld(B,B)). [back_rewrite(12),rewrite([260(4)])].
% 0.88/1.13 283 rd(A,ld(B,B)) = mult(A,ld(B,B)). [para(152(a,1),209(a,1,2)),rewrite([260(4),152(3)]),flip(a)].
% 0.88/1.13 285 mult(A,ld(A,mult(B,ld(B,ld(C,C))))) = mult(A,mult(ld(A,ld(B,B)),ld(C,C))). [back_rewrite(226),rewrite([283(3),211(3),82(7),193(5),211(3)])].
% 0.88/1.13 295 mult(mult(A,ld(B,B)),B) = mult(A,B). [para(280(a,1),260(a,1,1)),rewrite([256(6),21(5)])].
% 0.88/1.13 296 mult(A,mult(ld(A,ld(mult(B,C),mult(B,C))),ld(C,C))) = mult(A,ld(A,ld(mult(B,C),mult(B,C)))). [back_rewrite(270),rewrite([295(6),260(5),211(5)]),flip(a)].
% 0.88/1.13 299 mult(mult(A,ld(B,B)),ld(mult(A,ld(B,B)),B)) = ld(mult(A,ld(B,B)),mult(A,B)). [para(295(a,1),11(a,1,2)),flip(a)].
% 0.88/1.13 304 ld(A,mult(B,ld(mult(A,ld(A,B)),C))) = ld(A,C). [para(83(a,1),11(a,1,2)),rewrite([11(3),187(3),187(8)]),flip(a)].
% 0.88/1.13 305 mult(mult(A,B),ld(mult(A,B),C)) = mult(A,ld(A,C)). [para(11(a,1),83(a,1,2,2,2,1,2)),rewrite([84(4),140(6)])].
% 0.88/1.13 310 ld(mult(A,ld(B,B)),mult(A,B)) = mult(A,ld(A,B)). [back_rewrite(299),rewrite([305(6)]),flip(a)].
% 0.88/1.13 345 ld(mult(A,ld(A,B)),B) = mult(A,ld(A,ld(B,B))). [para(21(a,1),197(a,1,2))].
% 0.88/1.13 347 mult(A,ld(A,mult(B,ld(B,C)))) = mult(A,ld(A,C)). [para(84(a,1),197(a,1,2)),rewrite([197(4)]),flip(a)].
% 0.88/1.13 358 mult(A,mult(ld(A,ld(B,B)),ld(C,C))) = mult(A,ld(A,ld(C,C))). [back_rewrite(285),rewrite([347(5)]),flip(a)].
% 0.88/1.13 364 mult(A,ld(A,ld(mult(B,C),mult(B,C)))) = mult(A,ld(A,ld(C,C))). [back_rewrite(296),rewrite([358(7)]),flip(a)].
% 0.88/1.13 368 ld(mult(A,ld(A,B)),mult(A,ld(A,C))) = ld(mult(A,ld(A,B)),C). [para(11(a,1),199(a,1,1)),rewrite([11(7)])].
% 0.88/1.13 376 mult(ld(A,A),B) = mult(A,ld(A,B)). [para(211(a,1),295(a,1,1)),rewrite([82(4),45(2)]),flip(a)].
% 0.88/1.13 377 ld(ld(A,A),B) = mult(A,ld(A,B)). [para(211(a,1),140(a,1,2,2,1)),rewrite([82(6),376(4),347(6),199(5),376(4),196(4),376(5),82(6),376(4),347(6)])].
% 0.88/1.13 391 rd(mult(A,ld(A,B)),B) = mult(A,ld(A,ld(B,B))). [para(376(a,1),280(a,1,1)),rewrite([376(6)])].
% 0.88/1.13 392 ld(mult(A,ld(A,ld(B,B))),C) = mult(A,ld(A,C)). [para(82(a,1),377(a,2)),rewrite([368(5),345(3),304(9)])].
% 0.88/1.13 451 ld(A,mult(B,ld(B,C))) = ld(A,C). [para(376(a,1),304(a,1,2)),rewrite([392(4),347(4)])].
% 0.88/1.13 457 mult(A,mult(B,ld(B,C))) = mult(A,C). [para(451(a,1),84(a,1,2,2)),rewrite([84(3)]),flip(a)].
% 0.88/1.13 463 ld(mult(A,ld(A,B)),C) = mult(A,ld(A,ld(B,C))). [para(451(a,1),197(a,1))].
% 0.88/1.13 522 ld(mult(A,B),mult(A,B)) = mult(A,ld(A,ld(B,B))). [para(310(a,1),391(a,1,1,2)),rewrite([457(5),295(3),44(3),364(12),305(10)])].
% 0.88/1.13 690 ld(ld(A,B),ld(A,B)) = mult(A,ld(A,ld(B,B))). [para(196(a,1),522(a,2)),rewrite([451(5),463(3)]),flip(a)].
% 0.88/1.13 707 $F # answer(goals). [back_rewrite(277),rewrite([690(8),457(9)]),xx(a)].
% 0.88/1.13
% 0.88/1.13 % SZS output end Refutation
% 0.88/1.13 ============================== end of proof ==========================
% 0.88/1.13
% 0.88/1.13 ============================== STATISTICS ============================
% 0.88/1.13
% 0.88/1.13 Given=94. Generated=4223. Kept=694. proofs=1.
% 0.88/1.13 Usable=32. Sos=104. Demods=153. Limbo=17, Disabled=549. Hints=0.
% 0.88/1.13 Megabytes=0.82.
% 0.88/1.13 User_CPU=0.14, System_CPU=0.01, Wall_clock=0.
% 0.88/1.13
% 0.88/1.13 ============================== end of statistics =====================
% 0.88/1.13
% 0.88/1.13 ============================== end of search =========================
% 0.88/1.13
% 0.88/1.13 THEOREM PROVED
% 0.88/1.13 % SZS status Theorem
% 0.88/1.13
% 0.88/1.13 Exiting with 1 proof.
% 0.88/1.13
% 0.88/1.13 Process 16472 exit (max_proofs) Tue Jun 14 06:09:13 2022
% 0.88/1.13 Prover9 interrupted
%------------------------------------------------------------------------------